What were the reasons for America's neutrality in the beginning of World War I?

It was not their concern, basically. It was a war that was not of their making and was between two countries with whom America was friendly. They also had a lot to lose as both countries were good commercial partners and took a lot of American goods especially, but not exclusively, arms and munitions. As the previous answer implied there were a lot of Americans who were descended from both German and British stock and Americans owned many companies in both countries..

They were more likely to try to mediate as Alexander Haig tried so very hard to do between Britain and Argentina during the run up to the Falklands war.

It wanted to sell weapons to both sides, and it didn't want to get involved in a war that was so far away from it's territory, "Why waste American lives for a foreign war".

Many Americans were also descended from Germans. They wanted Germany to win so they tried to keep America out of the war so that Germany could take over Europe.